What is Addition Expression
Explanation : Addition Expression in algebra includes:
Literal Number,
Addition Operator (+)
and Constant
For example:
(x + y), (a + 7), (4 + b)
In the above example, we have :
Addition Operator i.e. plus sign (+),
Literal Numbers = x, y, a & b.
Constants = 7 & 4.
Addition expression in algebra is of the following two types:
1). Sum of Literal Numbers : It includes Addition Operator (+) and two or more Literal Numbers.
For example = x+y , p+q, a+b+c
In the above example we have :
Addition Operator = (+),
Literal Numbers =. x, y, p, q, a, b & c
Note : In such an expression, we don't have any Constants.
2). Sum of Literal Numbers and Constants : It includes Addition Operator (+), Literal Numbers and Constants.
For example = x+7 , 8+a, p+q+5...
In the above example we have :
Addition Operator = (+),
Literal Numbers = x, p, q & a.
Constants = 7, 8 & 5.
Addition of Algebraic Expressions
Before you further read, you are advice to read:
What are Terms of Algebraic Expression ?
What are Like Terms ?
What are Unlike Terms ?
Addition of Like Terms ?
During addition of algebraic expression we are encountered with the following three situations:
Addition of algebraic expression having like terms
Addition of algebraic expression having unlike terms
Addition of algebraic expression having both like and unlike terms
1) Addition of algebraic expression having like terms
Following are steps to be followed while adding two or more algebraic Expression having like terms:
Step 1: Rearrange the terms of given algebraic expression into liketerms
Step 2: Add like terms
Example : Add 2a + 3b  4x + 5y  6 and (7a  8b + 9x + 10y  11)
Solution: Given two algebraic expression
First Algebraic expression = 2a + 3b  4x + 5y  6
Second Algebraic expression = (7a  8b + 9x + 10y  11)
Now addition of given algebraic expression is done as follows:
(2a + 3b  4x + 5y  6) + (7a  8b + 9x + 10y  11)
Open brackets and we get:
= 2a + 3b  4x + 5y  6  7a  8b + 9x + 10y  11
Rearrange the terms of given algebraic expression into liketerms and we get:
= 2a  7a + 3b  8b  4x + 9x + 5y + 10y  6  11
Add like terms and we get:
= (5a  5b + 3x + 15y  17)
Hence, (2a + 3b  4x + 5y  6) + (7a  8b + 9x + 10y  11) = (5a  5b + 3x + 15y  17)
2) Addition of algebraic expression having unlike terms
Here we must note that two or more algebraic expressions are added only when both have unlike terms.
Or we can also say that:
Algebraic expressions having unlike terms cannot be added.
E.g. 2x  1 + 3z, 3y + 5t  9a + 5x^{2}, 10p + t^{3}  4b  8r, 32q  6m + 10c cannot be added because all have unlike terms.
3) Addition of algebraic expression having both like and unlike terms
In such situations you will notice that algebraic expressions which are to be added have like as well as unlike terms. So in such situations we add like terms and keep unlike terms as such.
Example : Add ( 2x^{3} + 3x^{2} + 10y  2), x^{3}  4x^{2} + 9x  c
Solution: Given two algebraic expression
First Algebraic expression =  2x^{3} + 3x^{2} + 10y  2
Second Algebraic expression = x^{3}  4x^{2} + 9x  c
Now addition of given algebraic expression is done as follows:
( 2x^{3} + 3x^{2} + 10y  2) + (x^{3}  4x^{2} + 9x  c)
Open brackets and we get:
=  2x^{3} + 3x^{2} + 10y  2 + x^{3}  4x^{2} + 9x  c
Rearrange them into like terms and unlike terms & we get
=  2x^{3} + x^{3} + 3x^{2}  4x^{2} + 10y + 9x  c  2
Add like terms and keep unlike terms as such & we get:
=  x^{3}  x^{2} + 10y + 9x  c  2
Hence, ( 2x^{3} + 3x^{2} + 10y  2) + (x^{3}  4x^{2} + 9x  c) = ( x^{3}  x^{2} + 10y + 9x  c  2)

